Control surface freeplay effects investigation on airfoil's aero-elastic behavior in the sub-sonic regime

One of the main limitations of linearity assumptions in airfoil’s aero-elastic problems is the inability to predict the system behavior after starting the instability. In reality, nonlinearities may prevent the amplitudes from going to infinity. This paper presents a methodological approach for predicting airfoil aero-elastic behavior to investigate the control surface freeplay effects on the state responses and the flutter speed. For this purpose, the airfoil structural model is firstly developed while using the Lagrange’s method. The aerodynamic model is then generated by utilizing the Theodorsen approach for lift and moment calculation and Jones approximation with P-method for unstable aerodynamic modelling. After that, the aero-elastic model is developed by combination of structural and aerodynamic models and a numerical integration method is used to extract the time responses in the state space. The flutter analysis has been completed by utilizing the P-method for the system without freeplay and by the time response approach for the system with freeplay. The results that were obtained from simulations confirm the effectiveness of the proposed method to predict the aero-elastic behavior and stability condition of a two-dimensional airfoil as well as to estimate the flutter speed with reasonable accuracy and low computational effort. Moreover, a sensitivity analysis of freeplay degree on time response results has been done and the results are discussed in detail. It is also showed that the control surface freeplay decreases the flutter speed. The results of the paper are also validated against publicly available data.